The Dynamic of the Suburban Railway Passenger
Transport in the Traffic System of the City of
Zagreb
Marijan Rajsman
Faculty of Transport and Traffic Sciences, University of Zagreb, Republic of Croatia
Email: [email protected]
Dražen Ratković and Helena Biškupić Grgačević
Email: [email protected] and [email protected]
Abstract— The subject of this paper is to research the
dynamic and the possibilities of modelling the development
of the passenger transport demand in the railway passenger
suburban traffic system of the City of Zagreb and the inland
railway passenger traffic in the Republic of Croatia. The
researched traffic sizes by their characteristics are
quantitative indicators of the railway passenger traffic
transport demand, stated by the number of transported
passengers and realised transport operation within the
system. The appropriate mathematical and statistical
analysis of passenger transport demand established the
existing condition on the level of the traffic system; then, a
mathematical and prognostic trend model of the researched
size development dynamic was made. The prognostic trend
model of the traffic size has been represented by an
appropriate equation, with the calculation of the
appertaining determination coefficient as a measure of
quality, establishing the level of statistical significance of the
given data description.
Index Terms— railway passenger demand, public urban and
suburban passenger transport system, growth, development
I.
INTRODUCTION
With regard to the firm correlation of the economic
and traffic development, a study on the functioning and
especially the dynamic of the development of the traffic
system represents a major subject of scientific and
research interest and work.
“Reference [1], [2]” The transport demand has a
crucial importance for the establishment and management
of the traffic policy; moreover, it is a basic factor
dimensioning the level of the traffic system development,
and consequently the degree of utilisation of its technical
stratum primarily, i.e. the traffic infrastructure and means
of transport.
The subject of this research consists in the research of
the dynamics and the possibility of modelling the
mathematical and prognostic model of the railway
Manuscript received November 25, 2014; revised Januray 2, 2015;
accepted January 13, 2015.
Marijan Rajsman, corresponding author
passenger demand in the traffic system of the City of
Zagreb.
The goal of the research consists in establishing the
principles according to which the passenger transport
demand receives their values within the function of time.
The research subject has been defined based on the
research problem, i.e. to research the transport demand in
the railway traffic system of the Republic of Croatia,
especially in the City of Zagreb, with the goal of forming
a mathematical transport demand prognostic trend model.
A basic scientific hypothesis has been made: based on the
conducted research, it is possible to scientifically
establish the principles of the studied traffic sizes in the
railway traffic system of the Republic of Croatia and the
City of Zagreb and to create a mathematical and
prognostic demand trend model for transportation
services within the passenger traffic.
“Reference [3]” The need to establish this hypothesis
ensues from the definition of the traffic system as a
complex dynamic system, which is subject to rules
according to the general system management theory,
whereby the implementation of a mathematical theory to
design the mathematical models of concrete problems is
necessary in the area of traffic and transport technology
for the traffic system and its subsystem management.
“Reference [4]” The traffic demand is of a stochastic
character so that within the modelling it is necessary to
use the methods of mathematical statistics and probability
theory, also establishing the trend of the traffic size
development. The trend represents a development
tendency of the traffic size in time and is represented by a
function of time. The transport modelling has a major
role in all complex decision-making processes, especially
with regard to the traffic development modelling. With
regard to the dynamics in the traffic analyses of the
changes in the economic and traffic system, analytical
methods detecting the changes in a shorter time period
are more desirable, so that the subject and the results of
the research and modelling are better directed.
The application of the results of this paper is reflected
in the following: a) the research results provide the
decision-makers on further development of the traffic
system in the studied area with a scientifically established
information on the past processes providing the traffic
sizes with their values, b) the applied value of this
research consists in shaping a theoretic model of the
traffic demand development, based on the results of the
traffic size research, i.e. in formulating a functional law
defining the tendency of change and direction of the
traffic size development process within the traffic system,
c) the results of the research of the studied values,
established laws, as well as formed mathematical models,
represent a scientifically established basis for making
decisions on the traffic system development and
management.
With regard to the applied method, it can be
established that the paper dealt with analytical modelling
of the passenger transport demand in which the models
are in an analytical form (e.g. equation systems), so that
the solutions are also in an analytical form. Moreover,
these are stochastic models, whose behaviour cannot be
predicted in advance, so that, therefore, probabilities of
change in the condition of the system are defined by
calculating the value of the determination coefficient.
Figure 1. Investment into railway infrastructure of the Republic of
Croatia for the period 2007 – 2017 (in HRK million)
Source: Hrvatske željeznice (Croatian Railways), Infrastruktura
(Infrastructure, Inc.) d.o.o., Zagreb, 2013
The system of public city and suburban passenger
transport is an integral part of the traffic system of
Central Croatia, in which the railways comprise one of
the basic transport systems (presented schematically in
Figure 2).
II. SIGNIFICANCE OF THE RAILWAY PASSENGER
TRANSPORT FOR THE TRAFFIC SYSTEM OF
THE CITY OF ZAGREB
Within the public city and suburban passenger
transport system of the City of Zagreb, the contribution of
the railway transport system is rather significant.
“Reference [5]” The contribution of the railways in
meeting the needs of the passenger demand in the traffic
system of the City of Zagreb is a consequence of the high
quality level of the transport service, significant transport
capacity and already known ecological advantages with
regard to other transport systems, especially compared to
the road traffic. The railway system significantly
contributes to meeting the needs of the transport demand
in a large number of European cities. Thus, according to
European practice, cities, municipalities, counties and the
state participate with approximately 60% in the structure
of the total costs of an integrated passenger transport,
while
railway
undertakings
participate
with
approximately 40% (average of German, French, Belgian
and Czech cities).
The investment in the Croatian railway infrastructure
as presented in Figure 1, in the period from 2008 to 2012,
was on average at the same level (approximately HRK
600-650 million per year) with a constant slight
downward trend. Only since 2013 is the investment surge
by more than three times evident with regard to the
previous year, with plans of almost exponential
investment growth by 2017.
Figure 2. Schematic presentation of the railway network in the traffic
system of Central Croatia
Source: Hrvatske željeznice (Croatian Railways), Infrastruktura
(Infrastructure, Inc.) d.o.o., Zagreb, 2013
Central Croatia is comprised of a wider gravitation area
of the City of Zagreb and the Zagreb County, as well as
the surrounding counties (including the Varaždin and
Međimurje counties); according to the territory that it
encompasses, it makes a third of the surface of the
Republic of Croatia; however, at the same time, almost a
half of the nation’s population lives in the area. Most
certainly, Central Croatia represents a generator of the
entire Croatian economic, social and political
development, so that the significance of the traffic system
functioning and developing in the area is thus even more
significant.
III. RAILWAY PASSENGER SUBURBAN
TRANSPORT OF THE CITY OF ZAGREB
The passenger railway suburban transport system has a
special meaning in the traffic system of the City of
Zagreb. Such a significance and the actual contribution of
the railways in meeting the needs of the passenger
transport needs is a consequence of several factors. The
railway lines are almost ideally placed along the EastWest traffic route, passing through the centre of the City
of Zagreb, that, apart from being the capital of the
Republic of Croatia, represents a hub of the central
Croatian region. Accordingly, the developed railway
network of the suburban lines can be promoted
additionally with a larger number of stops within not only
the suburban but also the urban area. Studying the
dynamic of the railway passenger transport demand, it
was established that the railway exists as a major
transport system incorporated in the traffic system of the
City of Zagreb.
“Reference [6]” Of special importance for the railway
passenger suburban transport system of the City of
Zagreb is the Savski Marof – Dugo Selo section (Figure
3). The section is in the Mediterranean corridor of the
TEN-T network and is used by passenger trains on
suburban, regional and international lines, as well as by
cargo trains in international and domestic traffic. About
400 trains of a rather heterogeneous structure are present
on the route daily, representing the most burdened part of
the Croatian railway network.
dominated by bus and tram transport system (within the
framework of Zagrebački Holding, the Zagrebački
Električni Tramvaj Subsidiary /Zagreb Electric Tram –
hereinafter: ZET d.o.o.) and the railway transport system
(Hrvatske željeznice Putnički prijevoz d.o.o./Croatian
Railways Passenger Transport – hereinafter: HŽPP).
With regard to the application of the common tariff union
since 1992, the users are able to use common passenger
tickets for ZET-HŽPP (see Figure 4).
Figure 4. Schematic presentation of tariff zones in which ZET-HŽPP
tickets apply
Source: HŽ Infrastruktura d.o.o., ((Croatian Railways, Infrastructure,
Inc.) 2013, according to Pintarić, Lj.: Osnovne karakteristike tržišta
željezničkoga gradsko-prigradskog putničkog prijevoza / Basic
Characteristics of the Urban and Suburban Railway Passenger Transport
Market, HŽ Infrastruktura d.o.o., Željeznice 21, No. 2, Zagreb, 2014, p.
21-30
Figure 3. Schematic presentation of the railway network within the
system of the city and suburban passenger transport of the City of
Zagreb
Source: HŽ Infrastruktura d.o.o., (Croatian Railways, Infrastructure,
Inc.) Zagreb, 2013
Legend:
Train station
Train stop
Train station used for urban and suburban transport
Railway line
Within the traffic system of the City of Zageb and its
gravitational area, the public passenger transport is
The system of the common ZET - HŽPP ticket,
according to the structure of its transport users, is mostly
comprised of workers with around 90% of the total
number of passengers, while within the remaining 10%
there are pupils, students, pensioners and social benefit
users. Further below we will present data on the
passenger demand and the realised suburban railway
passenger transport operation within the traffic system of
the City of Zagreb and on the domestic traffic within the
Croatian railway traffic system as well as its relative
share.
According to table 1, in the period 1995-2010, the
average annual rate of change in the passenger demand in
the domestic railway traffic at the level of the Republic of
Croatia amounted to +6.2%, while for the suburban
passenger traffic of the City of Zagreb it amounted to
10.5%. The analysis of the same time series for the
achieved passenger transport operation shows that the
average annual rate of change in the domestic railway
traffic on the level of the Republic of Croatia amounted
to +2.7%, while in the suburban passenger traffic of the
City of Zagreb it amounted to 9.4%. The share of the
suburban passenger railway traffic in the City of Zagreb
according to the number of transported passengers within
the domestic passenger traffic in that period has been
constantly increasing from the level of 40% to the level
of approximately 75% in 2008. After 2008 it was slightly
reduced to 72.6%. According to the achieved passenger
transport operation, the suburban passenger traffic of the
City of Zagreb was around 17.7%, while at the beginning
of the studied period it was up to 46.4% in the total
domestic passenger traffic.
prognostic trend of the studied variable is statistically
significant with the risk level p < 0.01.
TABLE I. PASSENGER TRANSPORT DEMAND AND REALISED
PASSENGER TRANSPORT OPERATION WITHIN DOMESTIC
RAILWAY TRAFFIC OF THE REPUBLIC OF CROATIA AS WELL
AS SUBURBAN RAILWAY PASSENGER TRAFFIC OF THE CITY
OF ZAGREB
Figure 5. The number of transported passengers in the suburban railway
traffic of the City of Zagreb
Y=2,911.4 x + 688.9
R2 = 0.801
(1)
(2)
Source: Transport and Communication, Statistical Reports in 2013, No.
1517, Croatian Bureau of Statistics, Zagreb, 2014
Note: achieved passenger transport operation expressed as PKM =
passenger kilometres
IV. THE DYNAMIC OF THE RAILWAY PASSENGER
TRANSPORT DEMAND IN THE TRAFFIC SYSTEM
OF THE CITY OF ZAGREB
The data on the number of transported passengers in
the suburban railway passenger lines in the traffic system
of the City of Zagreb have been processed further below
by methods of mathematical statistics by means of
Microsoft Excel; the data have been graphically presented
with appropriate diagrams. Except for the presentation of
the passenger demand in a diagram (expressed by a
number of transported passengers and realised passenger
transport operation) of the studied values, the appropriate
mathematical and statistical processing established the
prognostic trend models with the calculation of the
appertaining values of the determination coefficient for
each of the models. In this way, the evaluation of the
level of the statistical significance of each individual
model has been made possible.
The prognostic trend model of the development
dynamic of the studied traffic values has been obtained
by means of a computer programme, defined by a linear
trend model equation and a determination coefficient (R2)
as a measure of representation, while the dynamic has
been presented graphically as well. “Reference [7]” One
should note that beside the size of the sample analysed in
the paper (N = 16) the following applies: when the value
of the determination coefficient R2 is bigger than 0.388, it
follows that the established mathematical model of the
Figure 6. The realised passenger transport operation in the suburban
railway traffic of the City of Zagreb
Y= 43,062 x + 17.1
R2 = 0.789
(3)
(4)
Figure 7 Transported passengers in domestic railway traffic of the
Republic of Croatia
Y= 3062.2 x + 16,490
R2 = 0.798
(5)
(6)
The share of the suburban passenger traffic in the City of
Zagreb according to the number of transported passengers
in the domestic passenger traffic in that period has a
constant growth trend, relatively increasing from the level
of 40% to the level of approximately 75% in 2008.
According to the achieved passenger transport operation,
the suburban passenger traffic of the City of Zagreb was
about 17.7% at the beginning of the studied period up to
46.4% in the total domestic railway passenger traffic of
the Republic of Croatia.
By mathematical and statistical analysis of the
passenger transport demand in the period 1995-2010,
statistically significant trend models (p<0,01) have been
established for the studied values.
Figure 8. Realised passenger transport operation in domestic railway
transport of the Republic of Croatia
Y= 39,479 x + 926.18
R2 = 0.593
(7)
(8)
Statistically significant mathematical prognostic trend
models have been established for all the studied sizes
(p<0.01). The equations of these models have been
expressed in the text and marked with (1), (3), (5) and
(7).
V. CONCLUSION
The research has confirmed the scientific
hypothesis: based on the conducted study it is possible to
scientifically establish the principle of the studied traffic
values in the railway traffic system of the Republic of
Croatia and the City of Zagreb and to form a
mathematical prognostic trend model of the demand for
passenger traffic transport services. The established
mathematical prognostic trend models represent a
scientifically founded basis to forecast the need for
passenger transport in the railway transport system.
By analysing the passenger transport demand in the
suburban railway traffic of the City of Zagreb in the
studied period from 1995 to 2010, the following was
established: the average annual growth rate of passenger
transport demand was 10.5%, while the average annual
growth rate in the achieved passenger transport operation
was 9.4%.
The passenger transport demand in the domestic
railway passenger traffic of the Republic of Croatia in the
studied period from 1995 to 2010 grew with an average
annual growth rate in the passenger transport demand of
6.2%, i.e. 2.7% of the achieved passenger transport
operation.
It should also be mentioned that the intensity of the
increase in the passenger demand in that period in the
railway traffic of the City of Zagreb was 1.7 times bigger
compared to the total domestic passenger traffic of the
Republic of Croatia.
The growth intensity in the achieved passenger
transport operation was as much as 3.5 times bigger in the
suburban railway traffic of the City of Zagreb compared
to the domestic railway traffic of the Republic of Croatia.
REFERENCES
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– važne determinante prometne politike Hrvatske, Ceste i mostovi
(Transport Demand and Shape of the Space of the Croatian State –
Important Determinants of the Croatian Traffic Policy, Roads and
Bridges), no. 3-4, Zagreb, 2002, p. 71-80
[2] Rajsman M.: Model razvitka prometnog sustava Središnje Hrvatske
(Model of Development of the Traffic System of Central Croatia),
Doctoral dissertation, Faculty of Traffic Engineering, University of
Zagreb, 2005
[3] Radačić Ž.: Upravljanje složenim sustavima-s posebnim osvrtom na
prometni sustav (Managing Complex Systems with a Special View of
the Traffic System), postgraduate scientific study, authorised lectures,
Faculty of Traffic Engineering, University of Zagreb, Zagreb, 2000
[4] Hensher D. A., Button K.: Handbook of transport systems and traffic
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[5] Pintarić, Lj.: Osnovne karakteristike tržišta željezničkoga gradskoprigradskog putničkog prijevoza (Basic Characteristics of the Market of
Urban and Suburban Railway Passenger Transport), HŽ Infrastruktura
d.o.o., Željeznice 21, No. 2, Zagreb, 2014, p. 21-30
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Simulation of Railway Traffic at the Savski Marof – Dugo Selo Section
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Ph.D. Marijan Rajsman was born on May 15,
1959 in Vinkovci, Croatia, Married, two
children (son and daughter).
Education (academic status): from 2014
Associate Professor in the Area of Technical
Sciences, Scientific Field of Traffic and
Transport technologies - Faculty of Transport
and Traffic Sciences, University of Zagreb;
2013 Higher Scientific Researcher in the Area
of Technical Sciences, Scientific Field of
Traffic and Transport Technologies, University
of Zagreb; 2011 College Professor in the Area
of
Social
Sciences,
Scientific
Field of Economics; 2009 Assistant
Author’s formal poto
Professor in the Area of Technical Sciences, Scientific Field of Traffic
and Transport Technologies - Faculty of Transport and Traffic Sciences,
University of Zagreb; 2006 Scientific Researcher in the Area of
Technical Sciences, Scientific Field of Traffic and Transport
Technologies, University of Zagreb: 2005 Ph. D. at the Faculty of
Transport and Traffic Sciences in Zagreb, Croatia; 1983M. A. at the
Faculty of Transport and Traffic Sciences in Zagreb, Croatia
Professional career: from 2014 Associate Professor at the Faculty of
Transport and Traffic Sciences of the University of Zagreb; 2008 –
2012 extramural associate at the Faculty of Maritime Studies in Rijeka,
Croatia; 2011 – 2012 Acting Dean of Zagreb Business College, Zagreb;
2006 – 2007 Dean of Libertas Business College, Zagreb; 2004 – 2006
Head of Department of Automatic Traffic Control of the City of Zagreb;
2002 – 2004 Assistant to the Minister of Maritime Affairs, Transport
and Infrastructure - Chairman of the Board of Inspection of the
Ministry of Maritime Affairs, Transport and Infrastructure; 2000 – 2002
manager of “Autobusni kolodvor Zagreb” d.o.o. Zagreb; 2000 Deputy
Head at the Zagreb City Bureau for Development, Civil Engineering,
Residential and Communal Affairs and Transport; 1998 – 2000
Commercial Manager at “Robni terminali Zagreb”, d.o.o. Zagreb; 1994
– 1996 Director of “Transcroatia” d.d. Zagreb; 1990 – 1994 Republic
Inspector for Roads and Road Transportatio at the Ministry of Maritime
Affairs, Transport and Infrastructure, Road Transport Inspector in the
City of Zagreb; 1988 – 1990 Head of Development at “Panturist” d.d.
Osijek; 1987 – 1988 Vice-president of the Management Board of RO
“Polet” Vinkovci (Company for Passenger and Cargo Transportation);
1984 - 1987 Manager of Technical Workshop Business Unit
“Transport” at the Agricultural and Industrial Company PIK
“Vinkovci”.
Publications: authored multiple research and professional papers in the
area of transport and management, active participant in several scientific
and professional domestic and international conferences.
Dražen Ratković, B.Sc. was born on June 11,
1954 in Split, Croatia. He is married, three
children (two sons and daughter).
Education (academic status): 1981 graduated
from the Faculty of Transport and Traffic
Sciences, University of Zagreb.
Professional career: from December 3, 2012
– CEO at HŽ Putnički prijevoz; 2012 – Board
Member at HŽ Holding and Manager at HŽ
Putnički prijevoz; 2009 – 2012 Chief person in
charge of selling the rail line for freight traffic
and Tradeformal
and Transport
Integration project coordinator for the port of
Author’s
poto
Ploče and the Vc corridor; 2007 – 2009 Consultant to the Board of HŽ
Infrastruktura; 2004 – 2007 Consultant to the Board of Croatian
Railways; 2000 – 2004 Board Member at Croatian Railways and HZ
Infrastruktura Manager; 1999 – 2000 Assistant Manager at HŽ Cargo;
1996 – 1999 Executive Director of the Transportation Arrangement
Dept. at Croatian Railways; 1994 – 1996 Head of Regulatory Affairs
Dept. at Croatian Railways; 1991 – 1994 Head of Zagreb Zapadni
kolodvor; 1983 – 1991 Technologist and Head of Transport and
Commercial Affairs Dept. of ŽTP Zagreb (Željezničko-transportno
poduzeće Zagreb) in Zagreb Zapadni kolodvor; 1983 – Head of
Technical Culture Dept. at Narodna tehnika.
Other: He gave presentations and participated in numerous conferences
on rail-related issues in Croatia and abroad.
Helena Biškupić Grgačević, MSc was born on
May 29, 1977 in Zagreb, Croatia. She is
married, two children (son and daughter).
Education (academic status): 2012 –
postgraduate study at the Faculty of
Economics, University of Zagreb
Professional career: from October 2012 –
Head of Controlling Dept. at HŽ Putnički
prijevoz; from April to September 2012 –
Controlling Dept. Manager at HŽ Holding,
Head of Controlling Dept. at HŽ Putnički prijevoz and coordinator of
Author’s formal
the Restructuring
Plan of HŽ Holding; 2007 – 2012 Chief person in
photo
charge of controlling at HŽ Putnički prijevoz; 2003 – 2006 Head of
Calculation and Accounting Division at Croatian Railways; 2001 –
2003 Chief person in charge of controlling at Croatian Railways.
Other: She gave presentations and participated in numerous
conferences on rail-related issues in Croatia.